Question

Let A=$\left[\begin{array}{ccc}1& 3& 2\\ 2& 5& t\\ 4& 7-t& -6\end{array}\right]$, then the values of t for which inverse of A does not exist

• A. -2, 1
• B. 3, 2
• C. 2, -3
• D. 3, -1

Answer 1

Answer: (C)

We know that inverse of A does not exist
only when |A| = 0
$\therefore$ $\left|\begin{array}{ccc}1& 3& 2\\ 2& 5& t\\ 4& 7-t& -6\end{array}\right|$=0
$(-30-7t+t^2)-3(-12-4t)$
$+2(14-2t-20)=0$
$\Rightarrow -30-7t+t^2+36+12t-12-4t=0$
$\Rightarrow t^2+t-6=0\Rightarrow t^2+3t-2t-6=0$
$\Rightarrow t(t+3)-2(t+3)=0$
$\Rightarrow (t+3)(t-2)=0\Rightarrow t=2,-3$